A mathematical framework for comparison of intermittent versus continuous adaptive chemotherapy dosing in cancer

Chemotherapy resistance in cancer remains a barrier to curative therapy in advanced disease. Dosing of chemotherapy is often chosen based on the maximum tolerated dosing principle; drugs that are more toxic to normal tissue are typically given in on-off cycles, whereas those with little toxicity are dosed daily. When intratumoral cell-cell competition between sensitive and resistant cells drives chemotherapy resistance development, it has been proposed that adaptive chemotherapy dosing regimens, whereby a drug is given intermittently at a fixed-dose or continuously at a variable dose based on tumor size, may lengthen progression-free survival over traditional dosing. Indeed, in mathematical models using modified Lotka-Volterra systems to study dose timing, rapid competitive release of the resistant population and tumor outgrowth is apparent when cytotoxic chemotherapy is maximally dosed. This effect is ameliorated with continuous (dose modulation) or intermittent (dose skipping) adaptive therapy in mathematical models and experimentally, however, direct comparison between these two modalities has been limited. Here, we develop a mathematical framework to formally analyze intermittent adaptive therapy in the context of bang-bang control theory. We prove that continuous adaptive therapy is superior to intermittent adaptive therapy in its robustness to uncertainty in initial conditions, time to disease progression, and cumulative toxicity. We additionally show that under certain conditions, resistant population extinction is possible under adaptive therapy or fixed-dose continuous therapy. Here, continuous fixed-dose therapy is more robust to uncertainty in initial conditions than adaptive therapy, suggesting an advantage of traditional dosing paradigms.